Before the New Year welcomes a host of fresh blockbusters, art-house offerings and Oscar hopefuls, here’s a final look at 2013’s most notable Asian films.

Everett Collection

“Drug War” (China)

Johnnie To’s violent crime drama about a morally ambiguous Chinese cop (Sun Honglei) who uses questionable means to nab a Hong Kong drug dealer (Louis Koo) is peppered with taboo subjects that often don’t pass the watchful eyes of mainland China censors. But the director won official approval and still delivered a smart, darkly funny and discomforting thriller.

Wong Kar-wai’s take on the life of martial-arts master Ip Man reveals that kung fu is as much an intellectual pursuit as it is a sport of strength and physical superiority. Does it matter whether you’ve seen the versions for Asia, Europe or the U.S.? No. Contractually obligated or not, the auteur is welcome to re-edit his films as often as he wants. Come to think of it, comparing the different versions could make an ideal college course elective.

Anthony Chen’s Cannes-winning (Camera d’Or) debut feature follows the lives of a Singaporean family and their Filipina domestic helper during the Asian financial crisis of the late 1990s. The film may be, in the words of the director, “culturally specific,” but Mr. Chen’s contemplation on childhood memories, attachments and heartache — even a lock a hair unleashes a multitude of emotion — are universal themes.

Edko Films Ltd.

“Like Father, Like Son” (Japan)

A personally ambitious, professionally successful man (Masaharu Fukuyama) rejects his 6-year-old son after learning the boy was accidentally switched at birth with another child. Director Hirokazu Koreeda’s study of quiet emotional abuse — by way of an unsympathetic father — is just one fragile piece of this absorbing drama about two families trying to sort out their paths forward. This won the Jury Prize at Cannes.

Edko Films Ltd.

“The Missing Picture” (Cambodia)

Documentary filmmaker Rithy Panh brings striking detail to his childhood memories of living under the Khmer Rouge regime. In the absence of a photographic archive, he uses miniature clay figures to depict his family and their friends in scenes of both domestic tranquility and extreme brutality. The effect gives the film, which took top prize in the Un Certain Regard section at Cannes, a heightened sense of immediacy to the horrific events witnessed by Mr. Panh.

On the surface, this is a harrowing story of extreme family dysfunction involving adultery, incest and castration, but the dialogue-less film suggests director Kim Ki-duk is exploring something beyond the sadomasochism. His real intent was to question his own views on Korean culture and whether he could break some taboos. The answer, he discovered, was that audiences mostly thought he had crossed a line he shouldn’t have, which probably means he’ll continue to push the conventional norms in his next film.

Jay Chou’s musical — a love story between a good-natured hooligan and a proper young woman, and which he directed — may look Baz Luhrmann-inspired with its vivid set pieces, but the pop singer may just as well have been invoking Francis Ford Coppola’s ill-fated 1982 musical “One From the Heart.” This movie isn’t for everyone, but its imaginative movie-studio recreation of a seaside town and lively supporting cast made it a welcome summer treat for the willing.

Director Bong Joon-ho’s (mostly) English-language actioner about Earth’s last inhabitants struggling for survival aboard a train as it continuously circles the snow-covered planet has a cast that rivals a Hollywood blockbuster: Chris Evans, John Hurt, Tilda Swinton, Octavia Spencer and Ed Harris, plus Song Kang-ho. It’s fast-paced, philosophical and wickedly funny — and far superior to “Elysium,” the year’s other thriller about class conflicts in a dystopian near-future.

Fans of director Tsai Ming-liang found ample reason to embrace this film — which won the Grand Jury Prize at Venice — about man and his two young children living in ruin and with little chance of escaping to a better life. Employing a minimal amount of dialogue and extreme long takes, Mr. Tsai asks his audiences to experience the hopelessness of his destitute characters.

Family man Wei-chung (Richie Jen) is leading a seemingly happy and quiet life in Taipei with his wife and their 6-year-old son. There’s just one thing: He’s gay. Director Arvin Chen’s comedy of errors about a mild-mannered optical-shop manager coming out of the closet blends funny heartbreak with moments of whimsy for a thoughtful tale of a middle-age man coming to terms with adulthood and responsibility.